2014/07/21 by Anton M. Unakafov, Karsten Keller · 1 citation
Physics and Astronomy · Mathematics · #nlin.CD #math.DS
paper · pdf · doi:10.1016/j.physd.2013.11.015
published as Physica D: Nonlinear Phenomena, 269 (2014), 94-102
arxiv created 2014/07/21 · arxiv updated 2014/07/22
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given ordinal pattern. We observe that this quantity provides a good estimation of the Kolmogorov-Sinai entropy in many cases. In particular, the conditional entropy of ordinal patterns of a finite order coincides with the Kolmogorov-Sinai entropy for periodic dynamics and for Markov shifts over a binary alphabet. Finally, the conditional entropy of ordinal patterns is computationally simple and thus can be well applied to real-world data.